On Earth, an iceberg floats with 95% of its volume submerged. An iceberg with equal mass and volume discovered in an ocean of water on a celestial planet with a gravitation force 4 times that of Earth will have what volume submerged?
A) Less than 95%
B) 95%
C) Greater than 95%
D) 100% submerged
Explanation
This question is testing your understanding of buoyancy and its relationship to gravity. To solve this problem, you must set up an expression that compares the volume of the fluid displaced to the volume of the object. For a floating object, the only two forces acting on the object are the buoyant force and the force of gravity, which are equal and opposite. Therefore, the expression can be set up as follows:
Fb = Fg
ρfluidVdisplacedg = ρobjectVobjectg
As you can see, the gravitational constant g cancels out resulting in the expression:
ρfluidVdisplaced = ρobjectVobject
or
Vdisplaced / Vobject = ρobject / ρfluid
Thus, the iceberg will be submerged exactly 95% regardless of the force of gravity making B the correct answer.
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